Boe, I agree with you.
Janet, You seem very defensive over the replies we've given here, your first posting suggested you and your dh were about to order A to leave, and that really can't be on, when you offered him a home in the first place. I am unclear too, when you and dh discussed that A wouldn't stay very long, was he in on these discussions?
Can you think back to being a teenager? it's a very confusing time. I think most teenage boys will live as A is doing if they can, it's up to you and dh to work at breaking the cycle.
First it's important that you and dh decide HONESTLY between you what you want (for example, could dh be telling you he wants A to leave, but telling A something different, just to keep things calm?).
When that is decided you need to sit down together with A and tell him what you would like to happen. PLEASE don't just baldly tell him to get out. If you both really do want him to leave, Offer to help him find an alternative (perhaps with his other relatives). That may solve the problem.
You may find that, despite what he says in a heated argument, he really wants to stay, in which case you need to work out a compromise. point out his responsibilities, tell him what privileges he can have in return.
Make sure your dh knows how A treats you when he's out, and that he supports you. BUT make sure you are fair in your treatment of A. Don't be tempted to snipe at him when dh is out, because that lowers you to the same level.
I feel sorry for your situation, but also think it's a bit tough that this kid (which is what he still is, even tho' old enough to vote drink and marry) was sort of foisted on you cos his mother moved away.
As I said before, as your husbands son he is your family. Families often cause as much grief as joy over the course of your life, it's just part of life's rich tapestry.
This problem doesn't have a quick fix. you all need to learn to compromise.
I wish you lots of luck and patience.